ABSTRACT
This problem has attracted a number of researchers during last years. On one side this is a problem occurring in practice relatively often and on the other side it brings a number of interesting problems for theoretical statisticians. Parametric setup was considered by Hinkley (1970), Hinkley and Hinkley (1970), Cobb (1978), Worsley (1986), Yao Y. C. (1987) and Siegmund (1988). They dealt with the fixed changes only. Hinkley (1970) and Hinkley and Hinkley ( 1970) dealt with the maximum likelihood estimators when the observations are normally distributed. Assuming that the observations follow one-parameter exponential family distributions, Worsley (1986) derived both exact and approximate confidence regions for the change point based on the values accepted by a level a likelihood ratio tests. Cobb ( 1978) developed a method relying on a approximate ancillary statistics and applied it to the Nile data. Hinkley and Schechtman (1987) proposed various bootstrap schemes for the change point analysis. Siegmund (1988) discussed five types of confidence sets for the case when the distribution before and after the change are fully specified or have the distributions from an exponential family. Gombay and Horvath (1996) dealt with maximum likelihood estimators.
